While learning about spectral sequences a friend of mine found a proof of the snake lemma using spectral sequences. We noticed that the proof works equally well for larger bicomplexes. Particularly if you have an exact (anti)-commutative diagram enter image description here

you get an exact sequence enter image description here

We also have a little write-up of the proof here. We looked around, but couldn't find any reference to this anywhere, and no one else we talked to had really thought about it before. While toying with this we realized that the hypothesis is quite strong. That is, it is pretty difficult to find any interesting exact bicomplexes of the right size. I'm starting to suspect that there might not really be any interesting examples of this, and that that is the reason we haven't found anything about it anywhere.

So we're wondering, has anyone seen this before? Can anyone think of any non-trivial examples or applications of this?

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    $\begingroup$ This question is somewhat high level. You may have more luck getting an answer on Mathoverflow. $\endgroup$ – JoshuaZ May 4 at 12:52
  • $\begingroup$ Thank you I will repost it there then. $\endgroup$ – Jacob FG May 4 at 12:55

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